Cost and affordability of healthy diet (CoAHD) metrics developed in recent years have quickly become mainstream food security indicators among major development institutions, with the headline conclusion being that over 3 billion people worldwide cannot afford a healthy diet. Quantifying affordability constraints is indeed a vital addition to the suite of global food security indicators, opening up many opportunities to improve the accuracy and sensitivity of CoAHD methods for specific purposes. This paper provides three potentially useful extensions regarding the implications of accounting for: (1) differences in the age-sex structure across populations; (2) differences in non-food expenditure requirements across populations; and (3) differences and deficiencies in the representativeness of food price data. We apply these extensions to the cost and affordability of the EAT-Lancet reference diet, and find sizable sensitivity of baseline methods to adjusting diet affordability estimates for cross-country differences in demographic profiles and non-food expenditure requirements, smaller effects of adjusting for inadequate food product coverage in international price data, and inconclusive evidence on issues of urban bias in price surveys. Our proposed additions to current CoAHD methods significantly change country, regional and global estimates of healthy diet affordability, though not the headline conclusion that several billion people cannot afford a healthy diet. These and other extensions could be helpful to guide food system investments and policy choices in the years ahead, along with other improvements in the accuracy, rigor, and reliability of CoAHD statistics.